Modelling
Taavi Päll
17 10 2017
Estonian Land Board data
Available via www.maaamet.ee. API can be accessed programmatically using html requests. One can use “rvest” package. Please have a look at “R/maaamet.R” script in rstats-tartu/datasets repo. Returns html, but that ok too. Html results need little wrangling to get table.
Data that can be downloaded are number of transactions and price summaries per property size, and type for different time periods. Price info is given for data splits with more than 5 transactions.
Load dataset
## Check if file is alredy downloaded
if(!file.exists("data/transactions_residential_apartments.csv")){
url <- "https://raw.githubusercontent.com/rstats-tartu/datasets/master/transactions_residential_apartments.csv"
## Check if data folder is present
if(!dir.exists("data")){
dir.create("data")
}
## Download file to data folder
download.file(url, "data/transactions_residential_apartments.csv")
}Import
library(tidyverse)## Loading tidyverse: ggplot2
## Loading tidyverse: tibble
## Loading tidyverse: tidyr
## Loading tidyverse: readr
## Loading tidyverse: purrr
## Loading tidyverse: dplyr## Conflicts with tidy packages ----------------------------------------------## filter(): dplyr, stats
## lag(): dplyr, statslibrary(lubridate)##
## Attaching package: 'lubridate'## The following object is masked from 'package:base':
##
## datelibrary(stringr)
# Please try broom from GitHub as CRAN version may give obscure warning
# with augment
# devtools::install_github("dgrtwo/broom")
library(broom)
library(viridis)## Loading required package: viridisLiteapartments <- read_csv("data/transactions_residential_apartments.csv")## Parsed with column specification:
## cols(
## year = col_integer(),
## month = col_character(),
## county = col_character(),
## area = col_character(),
## transactions = col_integer(),
## area_total = col_double(),
## area_mean = col_double(),
## price_total = col_integer(),
## price_min = col_double(),
## price_max = col_double(),
## price_unit_area_min = col_double(),
## price_unit_area_max = col_double(),
## price_unit_area_median = col_double(),
## price_unit_area_mean = col_double(),
## price_unit_area_sd = col_double(),
## title = col_character(),
## subtitle = col_character()
## )## Warning in rbind(names(probs), probs_f): number of columns of result is not
## a multiple of vector length (arg 1)## Warning: 31 parsing failures.
## row # A tibble: 5 x 5 col row col expected actual expected <int> <chr> <chr> <chr> actual 1 11495 price_total no trailing characters e3 file 2 11504 price_total no trailing characters e3 row 3 11512 price_total no trailing characters e3 col 4 11513 price_total no trailing characters e3 expected 5 11573 price_total no trailing characters e3 actual # ... with 1 more variables: file <chr>
## ... ................. ... ................................................. ........ ................................................. ...... ................................................. .... ................................................. ... ................................................. ... ................................................. ........ ................................................. ...... .......................................
## See problems(...) for more details.apartments <- apartments %>%
mutate(date = ymd(str_c(year, month, 1, sep = "-"))) %>%
select(date, everything())
harju <- apartments %>% filter(str_detect(county, "Harju"))
harju## # A tibble: 890 x 18
## date year month county area transactions area_total
## <date> <int> <chr> <chr> <chr> <int> <dbl>
## 1 2005-01-01 2005 Jan Harju maakond 10-29,99 65 1418.8
## 2 2005-01-01 2005 Jan Harju maakond 30-40,99 155 5431.5
## 3 2005-01-01 2005 Jan Harju maakond 41-54,99 253 12043.8
## 4 2005-01-01 2005 Jan Harju maakond 55-69,99 230 14515.9
## 5 2005-01-01 2005 Jan Harju maakond 70-249,99 118 10905.0
## 6 2005-02-01 2005 Feb Harju maakond 10-29,99 63 1340.2
## 7 2005-02-01 2005 Feb Harju maakond 30-40,99 175 6125.2
## 8 2005-02-01 2005 Feb Harju maakond 41-54,99 257 12233.8
## 9 2005-02-01 2005 Feb Harju maakond 55-69,99 249 15659.0
## 10 2005-02-01 2005 Feb Harju maakond 70-249,99 174 15926.1
## # ... with 880 more rows, and 11 more variables: area_mean <dbl>,
## # price_total <int>, price_min <dbl>, price_max <dbl>,
## # price_unit_area_min <dbl>, price_unit_area_max <dbl>,
## # price_unit_area_median <dbl>, price_unit_area_mean <dbl>,
## # price_unit_area_sd <dbl>, title <chr>, subtitle <chr>Strategy
Start with single unit and identify interesting pattern
Summarise pattern with model
Apply model to all units
Look for units that don’t fit pattern
Summarise with single model
First glimpse
Plot number of transactions per year for Harju county and add smooth line.
p <- ggplot(harju, aes(factor(year), transactions, group = area, color = area)) +
geom_point() +
geom_smooth(method = 'loess') +
facet_wrap(~county, scales = "free_y") +
labs(
y = "Transactions",
x = "Year"
) +
scale_color_viridis(discrete = TRUE)
p
Mean price per unit area:
## Add date
p <- harju %>%
ggplot(aes(date, price_unit_area_mean, group = area, color = area)) +
geom_line() +
geom_vline(xintercept = ymd("2008-09-15"), linetype = 2) +
labs(title = "Transactions with residential apartments",
subtitle = "Harju county",
x = "Date",
y = bquote(Mean~price~(eur/m^2)),
caption = str_c("Source: Estonian Land Board, transactions database.\nDashed line, the collapse of the investment bank\nLehman Brothers on Sep 15, 2008.")) +
scale_color_viridis(discrete = TRUE, name = bquote(Apartment~size~m^2))
p
Adjust mean price to changes in consumer index:
download.file("https://raw.githubusercontent.com/rstats-tartu/datasets/master/consumer_index.csv",
"data/consumer_index.csv")
consumer_index <- read_csv("data/consumer_index.csv")## Warning: Missing column names filled in: 'X1' [1]## Parsed with column specification:
## cols(
## X1 = col_integer(),
## year = col_integer(),
## Jan = col_double(),
## Feb = col_double(),
## Mar = col_double(),
## Apr = col_double(),
## May = col_double(),
## Jun = col_double(),
## Jul = col_double(),
## Aug = col_double(),
## Sep = col_double(),
## Oct = col_double(),
## Nov = col_double(),
## Dec = col_double()
## )consumer_index## # A tibble: 22 x 14
## X1 year Jan Feb Mar Apr May Jun Jul Aug Sep
## <int> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 1996 61.86 63.84 64.90 66.02 66.35 66.74 66.94 66.28 66.55
## 2 2 1997 68.59 69.05 69.58 70.63 71.95 72.42 72.68 73.01 73.34
## 3 3 1998 76.50 77.23 77.89 78.22 78.48 78.68 79.14 79.01 78.88
## 4 4 1999 79.93 80.13 80.46 80.73 80.99 80.92 80.99 80.86 80.86
## 5 5 2000 82.37 82.44 83.03 83.10 83.23 83.50 84.29 84.35 84.68
## 6 6 2001 87.06 87.32 87.72 88.31 88.84 89.04 89.23 89.30 89.50
## 7 7 2002 90.75 91.28 91.54 92.33 92.53 92.46 92.14 91.74 91.87
## 8 8 2003 93.06 93.32 93.52 93.39 93.19 92.86 92.99 92.99 93.26
## 9 9 2004 93.65 93.85 94.18 94.77 96.62 96.95 96.69 96.62 96.82
## 10 10 2005 97.54 98.14 98.73 99.19 99.39 100.05 100.45 100.71 101.57
## # ... with 12 more rows, and 3 more variables: Oct <dbl>, Nov <dbl>,
## # Dec <dbl>## check if 2005 is 100%
consumer_index[10, 3:14] %>% rowMeans()## [1] 100divide_by_100 <- function(x) {
x/100
}
consumer_index <- consumer_index %>%
select(-X1) %>%
gather(key = month, value = consumerindex, -year) %>%
mutate_at("consumerindex", divide_by_100)
consumer_index## # A tibble: 264 x 3
## year month consumerindex
## <int> <chr> <dbl>
## 1 1996 Jan 0.6186
## 2 1997 Jan 0.6859
## 3 1998 Jan 0.7650
## 4 1999 Jan 0.7993
## 5 2000 Jan 0.8237
## 6 2001 Jan 0.8706
## 7 2002 Jan 0.9075
## 8 2003 Jan 0.9306
## 9 2004 Jan 0.9365
## 10 2005 Jan 0.9754
## # ... with 254 more rowsJoin apartments and consumer index data:
apartments <- left_join(apartments, consumer_index, by = c("year", "month"))Select harju county data:
harju_ci <- filter(apartments, str_detect(county, "Harju"))
harju_ci## # A tibble: 890 x 19
## date year month county area transactions area_total
## <date> <int> <chr> <chr> <chr> <int> <dbl>
## 1 2005-01-01 2005 Jan Harju maakond 10-29,99 65 1418.8
## 2 2005-01-01 2005 Jan Harju maakond 30-40,99 155 5431.5
## 3 2005-01-01 2005 Jan Harju maakond 41-54,99 253 12043.8
## 4 2005-01-01 2005 Jan Harju maakond 55-69,99 230 14515.9
## 5 2005-01-01 2005 Jan Harju maakond 70-249,99 118 10905.0
## 6 2005-02-01 2005 Feb Harju maakond 10-29,99 63 1340.2
## 7 2005-02-01 2005 Feb Harju maakond 30-40,99 175 6125.2
## 8 2005-02-01 2005 Feb Harju maakond 41-54,99 257 12233.8
## 9 2005-02-01 2005 Feb Harju maakond 55-69,99 249 15659.0
## 10 2005-02-01 2005 Feb Harju maakond 70-249,99 174 15926.1
## # ... with 880 more rows, and 12 more variables: area_mean <dbl>,
## # price_total <int>, price_min <dbl>, price_max <dbl>,
## # price_unit_area_min <dbl>, price_unit_area_max <dbl>,
## # price_unit_area_median <dbl>, price_unit_area_mean <dbl>,
## # price_unit_area_sd <dbl>, title <chr>, subtitle <chr>,
## # consumerindex <dbl>harju_ci <- harju_ci %>%
mutate(pua_mean_ci = price_unit_area_mean / consumerindex)Price per m^2 after consumer index adjustment:
harju_ci %>%
ggplot(aes(date, pua_mean_ci, group = area, color = area)) +
geom_line() +
geom_vline(xintercept = ymd("2008-09-15"), linetype = 2) +
labs(title = "Transactions with residential apartments",
subtitle = "Harju county",
x = "Date",
y = "Consumer index corrected mean price\nrelative to 2005 (eur/m^2)",
caption = str_c("Source: Estonian Land Board, transactions database.\nDashed line, the collapse of the investment bank\nLehman Brothers on Sep 15, 2008.")) +
scale_color_viridis(discrete = TRUE, name = bquote(Apartment~size~m^2))
Seasonal pattern
Seasonal pattern in number of transactions? Mean price eur/m^2 per month:
## Note that we are rearranging x axis using R builtin vector of month names
p <- harju %>%
ggplot(aes(factor(month, levels = month.abb), transactions, group = year)) +
geom_line(alpha = 0.3) +
geom_vline(xintercept = ymd("2008-09-15"), linetype = 2) +
facet_wrap(~ area, scales = "free_y") +
labs(title = "Seasonal trend in number of transactions\nwith residential apartments",
subtitle = "Harju county",
x = "Month",
y = "Transactions",
caption = "Source: Estonian Land Board, transactions database.") +
theme(axis.text.x = element_text(angle = 90, vjust = 0.5))
p
Add trendline per month. Fit linear model per month for each apartment size class. augment() function from “broom” library adds fitted values and residuals to the original data. We can use this to overlay model fit to our data.
predicted_transa <- harju %>%
lm(transactions ~ month + area, data = .) %>%
augment() # broom
predicted_transa %>%
arrange(desc(.cooksd)) %>%
dplyr::select(.cooksd, everything()) %>%
head## .cooksd transactions month area .fitted .se.fit .resid
## 1 0.02159508 530 Nov 41-54,99 258.5006 8.840215 271.4994
## 2 0.01811853 512 Oct 41-54,99 256.5092 8.613145 255.4908
## 3 0.01785884 461 Nov 55-69,99 214.1018 8.840215 246.8982
## 4 0.01776184 457 Dec 55-69,99 210.7732 8.840215 246.2268
## 5 0.01653771 492 Aug 41-54,99 247.9092 8.613145 244.0908
## 6 0.01528834 443 Sep 55-69,99 208.3103 8.613145 234.6897
## .hat .sigma .std.resid
## 1 0.01878010 63.87491 4.248853
## 2 0.01782772 63.95253 3.996386
## 3 0.01878010 63.99134 3.863856
## 4 0.01878010 63.99436 3.853348
## 5 0.01782772 64.00444 3.818068
## 6 0.01782772 64.04544 3.671015Overlay fitted values to previous plot.
p + geom_line(data = predicted_transa, aes(month, .fitted, group = 1),
color = "red",
size = 2) +
labs(caption = "Red line: model fit of seasonal effect to number of transactions.\nSource: Estonian Land Board, transactions database.")
The number of transactions increases during period from March to May?
Do we have similar effect to average price per m^2?
predicted_pua <- harju %>%
lm(price_unit_area_mean ~ month + area, data = .) %>%
augment()
predicted_pua %>% head## price_unit_area_mean month area .fitted .se.fit .resid
## 1 766.69 Jan 10-29,99 1167.756 36.6406 -401.0660
## 2 738.23 Jan 30-40,99 1143.193 36.6406 -404.9631
## 3 719.91 Jan 41-54,99 1159.304 36.6406 -439.3937
## 4 699.59 Jan 55-69,99 1166.595 36.6406 -467.0046
## 5 886.06 Jan 70-249,99 1347.656 36.6406 -461.5959
## 6 705.96 Feb 10-29,99 1175.696 36.6406 -469.7363
## .hat .sigma .cooksd .std.resid
## 1 0.01782772 274.2346 0.002467191 -1.474712
## 2 0.01782772 274.2279 0.002515370 -1.489042
## 3 0.01782772 274.1661 0.002961275 -1.615643
## 4 0.01782772 274.1129 0.003345132 -1.717167
## 5 0.01782772 274.1236 0.003268097 -1.697280
## 6 0.01782772 274.1074 0.003384381 -1.727212harju %>%
ggplot(aes(factor(month, levels = month.abb), price_unit_area_mean, group = year)) +
geom_line(alpha = 0.3) +
geom_vline(xintercept = ymd("2008-09-15"), linetype = 2) +
facet_wrap(~ area, scales = "free_y") +
labs(title = bquote(Seasonal~trend~price~per~m^2~of~residential~apartments),
subtitle = "Harju county",
x = "Month",
y = bquote(Mean~price~per~unit~area~(eur/m^2)),
caption = "Source: Estonian Land Board, transactions database.") +
theme(axis.text.x = element_text(angle = 90, vjust = 0.5)) +
geom_line(data = predicted_pua, aes(month, .fitted, group = 1),
color = "red",
size = 2)
Residuals? Add also year to model to visualise residuals.
predicted_trans2 <- harju %>%
lm(transactions ~ month + year + area, data = .) %>%
augment
predicted_trans2## transactions month year area .fitted .se.fit .resid
## 1 65 Jan 2005 10-29,99 88.58743 9.129342 -23.5874267
## 2 155 Jan 2005 30-40,99 153.91327 9.129342 1.0867306
## 3 253 Jan 2005 41-54,99 245.34585 9.129342 7.6541463
## 4 230 Jan 2005 55-69,99 200.94698 9.129342 29.0530227
## 5 118 Jan 2005 70-249,99 175.78967 9.129342 -57.7896739
## 6 63 Feb 2005 10-29,99 99.50743 9.129342 -36.5074267
## 7 175 Feb 2005 30-40,99 164.83327 9.129342 10.1667306
## 8 257 Feb 2005 41-54,99 256.26585 9.129342 0.7341463
## 9 249 Feb 2005 55-69,99 211.86698 9.129342 37.1330227
## 10 174 Feb 2005 70-249,99 186.70967 9.129342 -12.7096739
## 11 88 Mar 2005 10-29,99 125.02743 9.129342 -37.0274267
## 12 220 Mar 2005 30-40,99 190.35327 9.129342 29.6467306
## 13 350 Mar 2005 41-54,99 281.78585 9.129342 68.2141463
## 14 350 Mar 2005 55-69,99 237.38698 9.129342 112.6130227
## 15 199 Mar 2005 70-249,99 212.22967 9.129342 -13.2296739
## 16 101 Apr 2005 10-29,99 120.92076 9.129342 -19.9207601
## 17 202 Apr 2005 30-40,99 186.24660 9.129342 15.7533972
## 18 360 Apr 2005 41-54,99 277.67919 9.129342 82.3208130
## 19 329 Apr 2005 55-69,99 233.28031 9.129342 95.7196894
## 20 200 Apr 2005 70-249,99 208.12301 9.129342 -8.1230072
## 21 107 May 2005 10-29,99 123.94743 9.129342 -16.9474267
## 22 247 May 2005 30-40,99 189.27327 9.129342 57.7267306
## 23 404 May 2005 41-54,99 280.70585 9.129342 123.2941463
## 24 398 May 2005 55-69,99 236.30698 9.129342 161.6930227
## 25 226 May 2005 70-249,99 211.14967 9.129342 14.8503261
## 26 103 Jun 2005 10-29,99 106.98743 9.129342 -3.9874267
## 27 251 Jun 2005 30-40,99 172.31327 9.129342 78.6867306
## 28 408 Jun 2005 41-54,99 263.74585 9.129342 144.2541463
## 29 417 Jun 2005 55-69,99 219.34698 9.129342 197.6530227
## 30 232 Jun 2005 70-249,99 194.18967 9.129342 37.8103261
## 31 109 Jul 2005 10-29,99 111.74743 9.129342 -2.7474267
## 32 242 Jul 2005 30-40,99 177.07327 9.129342 64.9267306
## 33 422 Jul 2005 41-54,99 268.50585 9.129342 153.4941463
## 34 380 Jul 2005 55-69,99 224.10698 9.129342 155.8930227
## 35 241 Jul 2005 70-249,99 198.94967 9.129342 42.0503261
## 36 179 Aug 2005 10-29,99 119.45409 9.129342 59.5459066
## 37 297 Aug 2005 30-40,99 184.77994 9.129342 112.2200639
## 38 492 Aug 2005 41-54,99 276.21252 9.129342 215.7874796
## 39 421 Aug 2005 55-69,99 231.81364 9.129342 189.1863560
## 40 265 Aug 2005 70-249,99 206.65634 9.129342 58.3436594
## 41 177 Sep 2005 10-29,99 124.25409 9.129342 52.7459066
## 42 302 Sep 2005 30-40,99 189.57994 9.129342 112.4200639
## 43 472 Sep 2005 41-54,99 281.01252 9.129342 190.9874796
## 44 443 Sep 2005 55-69,99 236.61364 9.129342 206.3863560
## 45 281 Sep 2005 70-249,99 211.45634 9.129342 69.5436594
## 46 184 Oct 2005 10-29,99 128.05409 9.129342 55.9459066
## 47 334 Oct 2005 30-40,99 193.37994 9.129342 140.6200639
## 48 512 Oct 2005 41-54,99 284.81252 9.129342 227.1874796
## 49 411 Oct 2005 55-69,99 240.41364 9.129342 170.5863560
## 50 310 Oct 2005 70-249,99 215.25634 9.129342 94.7436594
## 51 166 Nov 2005 10-29,99 128.31564 9.243226 37.6843561
## 52 278 Nov 2005 30-40,99 193.64149 9.243226 84.3585134
## 53 530 Nov 2005 41-54,99 285.07407 9.243226 244.9259292
## 54 461 Nov 2005 55-69,99 240.67519 9.243226 220.3248056
## 55 338 Nov 2005 70-249,99 215.51789 9.243226 122.4821090
## 56 152 Dec 2005 10-29,99 124.98707 9.243226 27.0129276
## 57 323 Dec 2005 30-40,99 190.31292 9.243226 132.6870849
## 58 471 Dec 2005 41-54,99 281.74550 9.243226 189.2545006
## 59 457 Dec 2005 55-69,99 237.34662 9.243226 219.6533770
## 60 339 Dec 2005 70-249,99 212.18932 9.243226 126.8106804
## 61 129 Jan 2006 10-29,99 84.21063 8.912216 44.7893733
## 62 234 Jan 2006 30-40,99 149.53647 8.912216 84.4635306
## 63 447 Jan 2006 41-54,99 240.96905 8.912216 206.0309463
## 64 350 Jan 2006 55-69,99 196.57018 8.912216 153.4298227
## 65 229 Jan 2006 70-249,99 171.41287 8.912216 57.5871261
## 66 102 Feb 2006 10-29,99 95.13063 8.912216 6.8693733
## 67 190 Feb 2006 30-40,99 160.45647 8.912216 29.5435306
## 68 327 Feb 2006 41-54,99 251.88905 8.912216 75.1109463
## 69 321 Feb 2006 55-69,99 207.49018 8.912216 113.5098227
## 70 269 Feb 2006 70-249,99 182.33287 8.912216 86.6671261
## 71 178 Mar 2006 10-29,99 120.65063 8.912216 57.3493733
## 72 225 Mar 2006 30-40,99 185.97647 8.912216 39.0235306
## 73 414 Mar 2006 41-54,99 277.40905 8.912216 136.5909463
## 74 331 Mar 2006 55-69,99 233.01018 8.912216 97.9898227
## 75 272 Mar 2006 70-249,99 207.85287 8.912216 64.1471261
## 76 93 Apr 2006 10-29,99 116.54396 8.912216 -23.5439600
## 77 191 Apr 2006 30-40,99 181.86980 8.912216 9.1301973
## 78 288 Apr 2006 41-54,99 273.30239 8.912216 14.6976130
## 79 287 Apr 2006 55-69,99 228.90351 8.912216 58.0964894
## 80 235 Apr 2006 70-249,99 203.74621 8.912216 31.2537928
## 81 99 May 2006 10-29,99 119.57063 8.912216 -20.5706267
## 82 204 May 2006 30-40,99 184.89647 8.912216 19.1035306
## 83 362 May 2006 41-54,99 276.32905 8.912216 85.6709463
## 84 285 May 2006 55-69,99 231.93018 8.912216 53.0698227
## 85 232 May 2006 70-249,99 206.77287 8.912216 25.2271261
## 86 85 Jun 2006 10-29,99 102.61063 8.912216 -17.6106267
## 87 165 Jun 2006 30-40,99 167.93647 8.912216 -2.9364694
## 88 365 Jun 2006 41-54,99 259.36905 8.912216 105.6309463
## 89 285 Jun 2006 55-69,99 214.97018 8.912216 70.0298227
## 90 271 Jun 2006 70-249,99 189.81287 8.912216 81.1871261
## 91 84 Jul 2006 10-29,99 107.37063 8.912216 -23.3706267
## 92 180 Jul 2006 30-40,99 172.69647 8.912216 7.3035306
## 93 310 Jul 2006 41-54,99 264.12905 8.912216 45.8709463
## 94 278 Jul 2006 55-69,99 219.73018 8.912216 58.2698227
## 95 218 Jul 2006 70-249,99 194.57287 8.912216 23.4271261
## 96 139 Aug 2006 10-29,99 115.07729 8.912216 23.9227066
## 97 248 Aug 2006 30-40,99 180.40314 8.912216 67.5968639
## 98 426 Aug 2006 41-54,99 271.83572 8.912216 154.1642797
## 99 316 Aug 2006 55-69,99 227.43684 8.912216 88.5631561
## 100 243 Aug 2006 70-249,99 202.27954 8.912216 40.7204595
## 101 115 Sep 2006 10-29,99 119.87729 8.912216 -4.8772934
## 102 257 Sep 2006 30-40,99 185.20314 8.912216 71.7968639
## 103 395 Sep 2006 41-54,99 276.63572 8.912216 118.3642797
## 104 343 Sep 2006 55-69,99 232.23684 8.912216 110.7631561
## 105 271 Sep 2006 70-249,99 207.07954 8.912216 63.9204595
## 106 121 Oct 2006 10-29,99 123.67729 8.912216 -2.6772934
## 107 274 Oct 2006 30-40,99 189.00314 8.912216 84.9968639
## 108 476 Oct 2006 41-54,99 280.43572 8.912216 195.5642797
## 109 421 Oct 2006 55-69,99 236.03684 8.912216 184.9631561
## 110 309 Oct 2006 70-249,99 210.87954 8.912216 98.1204595
## 111 138 Nov 2006 10-29,99 123.93884 9.043198 14.0611562
## 112 308 Nov 2006 30-40,99 189.26469 9.043198 118.7353135
## 113 478 Nov 2006 41-54,99 280.69727 9.043198 197.3027292
## 114 367 Nov 2006 55-69,99 236.29839 9.043198 130.7016056
## 115 315 Nov 2006 70-249,99 211.14109 9.043198 103.8589090
## 116 119 Dec 2006 10-29,99 120.61027 9.043198 -1.6102724
## 117 240 Dec 2006 30-40,99 185.93612 9.043198 54.0638849
## 118 429 Dec 2006 41-54,99 277.36870 9.043198 151.6313006
## 119 363 Dec 2006 55-69,99 232.96982 9.043198 130.0301770
## 120 315 Dec 2006 70-249,99 207.81252 9.043198 107.1874804
## 121 99 Jan 2007 10-29,99 79.83383 8.727362 19.1661733
## 122 216 Jan 2007 30-40,99 145.15967 8.727362 70.8403306
## 123 342 Jan 2007 41-54,99 236.59225 8.727362 105.4077464
## 124 270 Jan 2007 55-69,99 192.19338 8.727362 77.8066228
## 125 219 Jan 2007 70-249,99 167.03607 8.727362 51.9639261
## 126 107 Feb 2007 10-29,99 90.75383 8.727362 16.2461733
## 127 239 Feb 2007 30-40,99 156.07967 8.727362 82.9203306
## 128 377 Feb 2007 41-54,99 247.51225 8.727362 129.4877464
## 129 297 Feb 2007 55-69,99 203.11338 8.727362 93.8866228
## 130 238 Feb 2007 70-249,99 177.95607 8.727362 60.0439261
## 131 122 Mar 2007 10-29,99 116.27383 8.727362 5.7261733
## 132 233 Mar 2007 30-40,99 181.59967 8.727362 51.4003306
## 133 457 Mar 2007 41-54,99 273.03225 8.727362 183.9677464
## 134 361 Mar 2007 55-69,99 228.63338 8.727362 132.3666228
## 135 258 Mar 2007 70-249,99 203.47607 8.727362 54.5239261
## 136 121 Apr 2007 10-29,99 112.16716 8.727362 8.8328400
## 137 261 Apr 2007 30-40,99 177.49300 8.727362 83.5069973
## 138 420 Apr 2007 41-54,99 268.92559 8.727362 151.0744130
## 139 322 Apr 2007 55-69,99 224.52671 8.727362 97.4732894
## 140 240 Apr 2007 70-249,99 199.36941 8.727362 40.6305928
## 141 120 May 2007 10-29,99 115.19383 8.727362 4.8061733
## 142 237 May 2007 30-40,99 180.51967 8.727362 56.4803306
## 143 414 May 2007 41-54,99 271.95225 8.727362 142.0477464
## 144 337 May 2007 55-69,99 227.55338 8.727362 109.4466228
## 145 305 May 2007 70-249,99 202.39607 8.727362 102.6039261
## 146 90 Jun 2007 10-29,99 98.23383 8.727362 -8.2338267
## 147 189 Jun 2007 30-40,99 163.55967 8.727362 25.4403306
## 148 312 Jun 2007 41-54,99 254.99225 8.727362 57.0077464
## 149 243 Jun 2007 55-69,99 210.59338 8.727362 32.4066228
## 150 205 Jun 2007 70-249,99 185.43607 8.727362 19.5639261
## 151 84 Jul 2007 10-29,99 102.99383 8.727362 -18.9938267
## 152 179 Jul 2007 30-40,99 168.31967 8.727362 10.6803306
## 153 304 Jul 2007 41-54,99 259.75225 8.727362 44.2477464
## 154 177 Jul 2007 55-69,99 215.35338 8.727362 -38.3533772
## 155 168 Jul 2007 70-249,99 190.19607 8.727362 -22.1960739
## 156 101 Aug 2007 10-29,99 110.70049 8.727362 -9.7004933
## 157 150 Aug 2007 30-40,99 176.02634 8.727362 -26.0263360
## 158 252 Aug 2007 41-54,99 267.45892 8.727362 -15.4589203
## 159 200 Aug 2007 55-69,99 223.06004 8.727362 -23.0600439
## 160 184 Aug 2007 70-249,99 197.90274 8.727362 -13.9027405
## 161 89 Sep 2007 10-29,99 115.50049 8.727362 -26.5004933
## 162 138 Sep 2007 30-40,99 180.82634 8.727362 -42.8263360
## 163 255 Sep 2007 41-54,99 272.25892 8.727362 -17.2589203
## 164 206 Sep 2007 55-69,99 227.86004 8.727362 -21.8600439
## 165 148 Sep 2007 70-249,99 202.70274 8.727362 -54.7027405
## 166 95 Oct 2007 10-29,99 119.30049 8.727362 -24.3004933
## 167 174 Oct 2007 30-40,99 184.62634 8.727362 -10.6263360
## 168 263 Oct 2007 41-54,99 276.05892 8.727362 -13.0589203
## 169 229 Oct 2007 55-69,99 231.66004 8.727362 -2.6600439
## 170 205 Oct 2007 70-249,99 206.50274 8.727362 -1.5027405
## 171 90 Nov 2007 10-29,99 119.56204 8.875706 -29.5620438
## 172 156 Nov 2007 30-40,99 184.88789 8.875706 -28.8878865
## 173 266 Nov 2007 41-54,99 276.32047 8.875706 -10.3204708
## 174 220 Nov 2007 55-69,99 231.92159 8.875706 -11.9215944
## 175 156 Nov 2007 70-249,99 206.76429 8.875706 -50.7642910
## 176 57 Dec 2007 10-29,99 116.23347 8.875706 -59.2334724
## 177 121 Dec 2007 30-40,99 181.55932 8.875706 -60.5593151
## 178 234 Dec 2007 41-54,99 272.99190 8.875706 -38.9918993
## 179 195 Dec 2007 55-69,99 228.59302 8.875706 -33.5930229
## 180 136 Dec 2007 70-249,99 203.43572 8.875706 -67.4357196
## 181 77 Jan 2008 10-29,99 75.45703 8.576865 1.5429734
## 182 118 Jan 2008 30-40,99 140.78287 8.576865 -22.7828693
## 183 194 Jan 2008 41-54,99 232.21545 8.576865 -38.2154536
## 184 158 Jan 2008 55-69,99 187.81658 8.576865 -29.8165772
## 185 116 Jan 2008 70-249,99 162.65927 8.576865 -46.6592738
## 186 64 Feb 2008 10-29,99 86.37703 8.576865 -22.3770266
## 187 134 Feb 2008 30-40,99 151.70287 8.576865 -17.7028693
## 188 237 Feb 2008 41-54,99 243.13545 8.576865 -6.1354536
## 189 181 Feb 2008 55-69,99 198.73658 8.576865 -17.7365772
## 190 158 Feb 2008 70-249,99 173.57927 8.576865 -15.5792738
## 191 70 Mar 2008 10-29,99 111.89703 8.576865 -41.8970266
## 192 112 Mar 2008 30-40,99 177.22287 8.576865 -65.2228693
## 193 236 Mar 2008 41-54,99 268.65545 8.576865 -32.6554536
## 194 214 Mar 2008 55-69,99 224.25658 8.576865 -10.2565772
## 195 181 Mar 2008 70-249,99 199.09927 8.576865 -18.0992738
## 196 82 Apr 2008 10-29,99 107.79036 8.576865 -25.7903600
## 197 166 Apr 2008 30-40,99 173.11620 8.576865 -7.1162027
## 198 239 Apr 2008 41-54,99 264.54879 8.576865 -25.5487869
## 199 221 Apr 2008 55-69,99 220.14991 8.576865 0.8500895
## 200 193 Apr 2008 70-249,99 194.99261 8.576865 -1.9926072
## 201 54 May 2008 10-29,99 110.81703 8.576865 -56.8170266
## 202 140 May 2008 30-40,99 176.14287 8.576865 -36.1428693
## 203 223 May 2008 41-54,99 267.57545 8.576865 -44.5754536
## 204 218 May 2008 55-69,99 223.17658 8.576865 -5.1765772
## 205 150 May 2008 70-249,99 198.01927 8.576865 -48.0192738
## 206 77 Jun 2008 10-29,99 93.85703 8.576865 -16.8570266
## 207 108 Jun 2008 30-40,99 159.18287 8.576865 -51.1828693
## 208 190 Jun 2008 41-54,99 250.61545 8.576865 -60.6154536
## 209 143 Jun 2008 55-69,99 206.21658 8.576865 -63.2165772
## 210 163 Jun 2008 70-249,99 181.05927 8.576865 -18.0592738
## 211 56 Jul 2008 10-29,99 98.61703 8.576865 -42.6170266
## 212 152 Jul 2008 30-40,99 163.94287 8.576865 -11.9428693
## 213 209 Jul 2008 41-54,99 255.37545 8.576865 -46.3754536
## 214 177 Jul 2008 55-69,99 210.97658 8.576865 -33.9765772
## 215 152 Jul 2008 70-249,99 185.81927 8.576865 -33.8192738
## 216 76 Aug 2008 10-29,99 106.32369 8.576865 -30.3236933
## 217 94 Aug 2008 30-40,99 171.64954 8.576865 -77.6495360
## 218 174 Aug 2008 41-54,99 263.08212 8.576865 -89.0821203
## 219 161 Aug 2008 55-69,99 218.68324 8.576865 -57.6832439
## 220 110 Aug 2008 70-249,99 193.52594 8.576865 -83.5259405
## 221 75 Sep 2008 10-29,99 111.12369 8.576865 -36.1236933
## 222 101 Sep 2008 30-40,99 176.44954 8.576865 -75.4495360
## 223 205 Sep 2008 41-54,99 267.88212 8.576865 -62.8821203
## 224 151 Sep 2008 55-69,99 223.48324 8.576865 -72.4832439
## 225 150 Sep 2008 70-249,99 198.32594 8.576865 -48.3259405
## 226 69 Oct 2008 10-29,99 114.92369 8.576865 -45.9236933
## 227 109 Oct 2008 30-40,99 180.24954 8.576865 -71.2495360
## 228 188 Oct 2008 41-54,99 271.68212 8.576865 -83.6821203
## 229 154 Oct 2008 55-69,99 227.28324 8.576865 -73.2832439
## 230 148 Oct 2008 70-249,99 202.12594 8.576865 -54.1259405
## 231 42 Nov 2008 10-29,99 115.18524 8.742620 -73.1852438
## 232 94 Nov 2008 30-40,99 180.51109 8.742620 -86.5110865
## 233 113 Nov 2008 41-54,99 271.94367 8.742620 -158.9436707
## 234 125 Nov 2008 55-69,99 227.54479 8.742620 -102.5447943
## 235 100 Nov 2008 70-249,99 202.38749 8.742620 -102.3874909
## 236 49 Dec 2008 10-29,99 111.85667 8.742620 -62.8566723
## 237 67 Dec 2008 30-40,99 177.18252 8.742620 -110.1825150
## 238 140 Dec 2008 41-54,99 268.61510 8.742620 -128.6150993
## 239 100 Dec 2008 55-69,99 224.21622 8.742620 -124.2162229
## 240 113 Dec 2008 70-249,99 199.05892 8.742620 -86.0589195
## 241 23 Jan 2009 10-29,99 71.08023 8.462559 -48.0802266
## 242 64 Jan 2009 30-40,99 136.40607 8.462559 -72.4060693
## 243 80 Jan 2009 41-54,99 227.83865 8.462559 -147.8386536
## 244 68 Jan 2009 55-69,99 183.43978 8.462559 -115.4397772
## 245 88 Jan 2009 70-249,99 158.28247 8.462559 -70.2824738
## 246 49 Feb 2009 10-29,99 82.00023 8.462559 -33.0002266
## 247 60 Feb 2009 30-40,99 147.32607 8.462559 -87.3260693
## 248 85 Feb 2009 41-54,99 238.75865 8.462559 -153.7586536
## 249 89 Feb 2009 55-69,99 194.35978 8.462559 -105.3597772
## 250 82 Feb 2009 70-249,99 169.20247 8.462559 -87.2024738
## 251 56 Mar 2009 10-29,99 107.52023 8.462559 -51.5202266
## 252 58 Mar 2009 30-40,99 172.84607 8.462559 -114.8460693
## 253 95 Mar 2009 41-54,99 264.27865 8.462559 -169.2786536
## 254 89 Mar 2009 55-69,99 219.87978 8.462559 -130.8797772
## 255 79 Mar 2009 70-249,99 194.72247 8.462559 -115.7224738
## 256 30 Apr 2009 10-29,99 103.41356 8.462559 -73.4135599
## 257 83 Apr 2009 30-40,99 168.73940 8.462559 -85.7394026
## 258 112 Apr 2009 41-54,99 260.17199 8.462559 -148.1719869
## 259 146 Apr 2009 55-69,99 215.77311 8.462559 -69.7731105
## 260 112 Apr 2009 70-249,99 190.61581 8.462559 -78.6158071
## 261 36 May 2009 10-29,99 106.44023 8.462559 -70.4402266
## 262 79 May 2009 30-40,99 171.76607 8.462559 -92.7660693
## 263 104 May 2009 41-54,99 263.19865 8.462559 -159.1986536
## 264 76 May 2009 55-69,99 218.79978 8.462559 -142.7997772
## 265 99 May 2009 70-249,99 193.64247 8.462559 -94.6424738
## 266 48 Jun 2009 10-29,99 89.48023 8.462559 -41.4802266
## 267 82 Jun 2009 30-40,99 154.80607 8.462559 -72.8060693
## 268 100 Jun 2009 41-54,99 246.23865 8.462559 -146.2386536
## 269 97 Jun 2009 55-69,99 201.83978 8.462559 -104.8397772
## 270 97 Jun 2009 70-249,99 176.68247 8.462559 -79.6824738
## 271 79 Jul 2009 10-29,99 94.24023 8.462559 -15.2402266
## 272 92 Jul 2009 30-40,99 159.56607 8.462559 -67.5660693
## 273 171 Jul 2009 41-54,99 250.99865 8.462559 -79.9986536
## 274 134 Jul 2009 55-69,99 206.59978 8.462559 -72.5997772
## 275 101 Jul 2009 70-249,99 181.44247 8.462559 -80.4424738
## 276 56 Aug 2009 10-29,99 101.94689 8.462559 -45.9468933
## 277 74 Aug 2009 30-40,99 167.27274 8.462559 -93.2727360
## 278 117 Aug 2009 41-54,99 258.70532 8.462559 -141.7053202
## 279 121 Aug 2009 55-69,99 214.30644 8.462559 -93.3064438
## 280 100 Aug 2009 70-249,99 189.14914 8.462559 -89.1491405
## 281 62 Sep 2009 10-29,99 106.74689 8.462559 -44.7468933
## 282 124 Sep 2009 30-40,99 172.07274 8.462559 -48.0727360
## 283 158 Sep 2009 41-54,99 263.50532 8.462559 -105.5053202
## 284 133 Sep 2009 55-69,99 219.10644 8.462559 -86.1064438
## 285 107 Sep 2009 70-249,99 193.94914 8.462559 -86.9491405
## 286 71 Oct 2009 10-29,99 110.54689 8.462559 -39.5468933
## 287 114 Oct 2009 30-40,99 175.87274 8.462559 -61.8727360
## 288 169 Oct 2009 41-54,99 267.30532 8.462559 -98.3053202
## 289 169 Oct 2009 55-69,99 222.90644 8.462559 -53.9064438
## 290 123 Oct 2009 70-249,99 197.74914 8.462559 -74.7491405
## 291 68 Nov 2009 10-29,99 110.80844 8.645530 -42.8084437
## 292 114 Nov 2009 30-40,99 176.13429 8.645530 -62.1342864
## 293 175 Nov 2009 41-54,99 267.56687 8.645530 -92.5668707
## 294 113 Nov 2009 55-69,99 223.16799 8.645530 -110.1679943
## 295 153 Nov 2009 70-249,99 198.01069 8.645530 -45.0106909
## 296 69 Dec 2009 10-29,99 107.47987 8.645530 -38.4798723
## 297 118 Dec 2009 30-40,99 172.80571 8.645530 -54.8057150
## 298 159 Dec 2009 41-54,99 264.23830 8.645530 -105.2382993
## 299 139 Dec 2009 55-69,99 219.83942 8.645530 -80.8394229
## 300 120 Dec 2009 70-249,99 194.68212 8.645530 -74.6821195
## 301 41 Jan 2010 10-29,99 66.70343 8.385924 -25.7034266
## 302 72 Jan 2010 30-40,99 132.02927 8.385924 -60.0292693
## 303 120 Jan 2010 41-54,99 223.46185 8.385924 -103.4618535
## 304 98 Jan 2010 55-69,99 179.06298 8.385924 -81.0629771
## 305 99 Jan 2010 70-249,99 153.90567 8.385924 -54.9056738
## 306 56 Feb 2010 10-29,99 77.62343 8.385924 -21.6234266
## 307 111 Feb 2010 30-40,99 142.94927 8.385924 -31.9492693
## 308 125 Feb 2010 41-54,99 234.38185 8.385924 -109.3818535
## 309 113 Feb 2010 55-69,99 189.98298 8.385924 -76.9829771
## 310 94 Feb 2010 70-249,99 164.82567 8.385924 -70.8256738
## 311 92 Mar 2010 10-29,99 103.14343 8.385924 -11.1434266
## 312 126 Mar 2010 30-40,99 168.46927 8.385924 -42.4692693
## 313 160 Mar 2010 41-54,99 259.90185 8.385924 -99.9018535
## 314 133 Mar 2010 55-69,99 215.50298 8.385924 -82.5029771
## 315 106 Mar 2010 70-249,99 190.34567 8.385924 -84.3456738
## 316 84 Apr 2010 10-29,99 99.03676 8.385924 -15.0367599
## 317 158 Apr 2010 30-40,99 164.36260 8.385924 -6.3626026
## 318 154 Apr 2010 41-54,99 255.79519 8.385924 -101.7951869
## 319 160 Apr 2010 55-69,99 211.39631 8.385924 -51.3963105
## 320 102 Apr 2010 70-249,99 186.23901 8.385924 -84.2390071
## 321 63 May 2010 10-29,99 102.06343 8.385924 -39.0634266
## 322 157 May 2010 30-40,99 167.38927 8.385924 -10.3892693
## 323 163 May 2010 41-54,99 258.82185 8.385924 -95.8218535
## 324 150 May 2010 55-69,99 214.42298 8.385924 -64.4229771
## 325 124 May 2010 70-249,99 189.26567 8.385924 -65.2656738
## 326 56 Jun 2010 10-29,99 85.10343 8.385924 -29.1034266
## 327 124 Jun 2010 30-40,99 150.42927 8.385924 -26.4292693
## 328 159 Jun 2010 41-54,99 241.86185 8.385924 -82.8618535
## 329 122 Jun 2010 55-69,99 197.46298 8.385924 -75.4629771
## 330 115 Jun 2010 70-249,99 172.30567 8.385924 -57.3056738
## 331 66 Jul 2010 10-29,99 89.86343 8.385924 -23.8634266
## 332 116 Jul 2010 30-40,99 155.18927 8.385924 -39.1892693
## 333 136 Jul 2010 41-54,99 246.62185 8.385924 -110.6218535
## 334 158 Jul 2010 55-69,99 202.22298 8.385924 -44.2229771
## 335 102 Jul 2010 70-249,99 177.06567 8.385924 -75.0656738
## 336 64 Aug 2010 10-29,99 97.57009 8.385924 -33.5700932
## 337 92 Aug 2010 30-40,99 162.89594 8.385924 -70.8959359
## 338 138 Aug 2010 41-54,99 254.32852 8.385924 -116.3285202
## 339 135 Aug 2010 55-69,99 209.92964 8.385924 -74.9296438
## 340 91 Aug 2010 70-249,99 184.77234 8.385924 -93.7723404
## 341 76 Sep 2010 10-29,99 102.37009 8.385924 -26.3700932
## 342 121 Sep 2010 30-40,99 167.69594 8.385924 -46.6959359
## 343 179 Sep 2010 41-54,99 259.12852 8.385924 -80.1285202
## 344 143 Sep 2010 55-69,99 214.72964 8.385924 -71.7296438
## 345 122 Sep 2010 70-249,99 189.57234 8.385924 -67.5723404
## 346 72 Oct 2010 10-29,99 106.17009 8.385924 -34.1700932
## 347 122 Oct 2010 30-40,99 171.49594 8.385924 -49.4959359
## 348 153 Oct 2010 41-54,99 262.92852 8.385924 -109.9285202
## 349 118 Oct 2010 55-69,99 218.52964 8.385924 -100.5296438
## 350 124 Oct 2010 70-249,99 193.37234 8.385924 -69.3723404
## 351 93 Nov 2010 10-29,99 106.43164 8.585657 -13.4316437
## 352 130 Nov 2010 30-40,99 171.75749 8.585657 -41.7574864
## 353 211 Nov 2010 41-54,99 263.19007 8.585657 -52.1900707
## 354 149 Nov 2010 55-69,99 218.79119 8.585657 -69.7911943
## 355 138 Nov 2010 70-249,99 193.63389 8.585657 -55.6338909
## 356 113 Dec 2010 10-29,99 103.10307 8.585657 9.8969277
## 357 121 Dec 2010 30-40,99 168.42891 8.585657 -47.4289150
## 358 163 Dec 2010 41-54,99 259.86150 8.585657 -96.8614992
## 359 165 Dec 2010 55-69,99 215.46262 8.585657 -50.4626228
## 360 136 Dec 2010 70-249,99 190.30532 8.585657 -54.3053195
## 361 44 Jan 2011 10-29,99 62.32663 8.347999 -18.3266265
## 362 84 Jan 2011 30-40,99 127.65247 8.347999 -43.6524692
## 363 109 Jan 2011 41-54,99 219.08505 8.347999 -110.0850535
## 364 90 Jan 2011 55-69,99 174.68618 8.347999 -84.6861771
## 365 76 Jan 2011 70-249,99 149.52887 8.347999 -73.5288737
## 366 44 Feb 2011 10-29,99 73.24663 8.347999 -29.2466265
## 367 88 Feb 2011 30-40,99 138.57247 8.347999 -50.5724692
## 368 122 Feb 2011 41-54,99 230.00505 8.347999 -108.0050535
## 369 97 Feb 2011 55-69,99 185.60618 8.347999 -88.6061771
## 370 110 Feb 2011 70-249,99 160.44887 8.347999 -50.4488737
## 371 97 Mar 2011 10-29,99 98.76663 8.347999 -1.7666265
## 372 103 Mar 2011 30-40,99 164.09247 8.347999 -61.0924692
## 373 149 Mar 2011 41-54,99 255.52505 8.347999 -106.5250535
## 374 120 Mar 2011 55-69,99 211.12618 8.347999 -91.1261771
## 375 109 Mar 2011 70-249,99 185.96887 8.347999 -76.9688737
## 376 50 Apr 2011 10-29,99 94.65996 8.347999 -44.6599599
## 377 100 Apr 2011 30-40,99 159.98580 8.347999 -59.9858026
## 378 146 Apr 2011 41-54,99 251.41839 8.347999 -105.4183868
## 379 120 Apr 2011 55-69,99 207.01951 8.347999 -87.0195104
## 380 117 Apr 2011 70-249,99 181.86221 8.347999 -64.8622071
## 381 76 May 2011 10-29,99 97.68663 8.347999 -21.6866265
## 382 100 May 2011 30-40,99 163.01247 8.347999 -63.0124692
## 383 143 May 2011 41-54,99 254.44505 8.347999 -111.4450535
## 384 122 May 2011 55-69,99 210.04618 8.347999 -88.0461771
## 385 117 May 2011 70-249,99 184.88887 8.347999 -67.8888737
## 386 46 Jun 2011 10-29,99 80.72663 8.347999 -34.7266265
## 387 115 Jun 2011 30-40,99 146.05247 8.347999 -31.0524692
## 388 168 Jun 2011 41-54,99 237.48505 8.347999 -69.4850535
## 389 119 Jun 2011 55-69,99 193.08618 8.347999 -74.0861771
## 390 125 Jun 2011 70-249,99 167.92887 8.347999 -42.9288737
## 391 47 Jul 2011 10-29,99 85.48663 8.347999 -38.4866265
## 392 90 Jul 2011 30-40,99 150.81247 8.347999 -60.8124692
## 393 155 Jul 2011 41-54,99 242.24505 8.347999 -87.2450535
## 394 119 Jul 2011 55-69,99 197.84618 8.347999 -78.8461771
## 395 95 Jul 2011 70-249,99 172.68887 8.347999 -77.6888737
## 396 69 Aug 2011 10-29,99 93.19329 8.347999 -24.1932932
## 397 131 Aug 2011 30-40,99 158.51914 8.347999 -27.5191359
## 398 196 Aug 2011 41-54,99 249.95172 8.347999 -53.9517202
## 399 133 Aug 2011 55-69,99 205.55284 8.347999 -72.5528438
## 400 127 Aug 2011 70-249,99 180.39554 8.347999 -53.3955404
## 401 65 Sep 2011 10-29,99 97.99329 8.347999 -32.9932932
## 402 125 Sep 2011 30-40,99 163.31914 8.347999 -38.3191359
## 403 153 Sep 2011 41-54,99 254.75172 8.347999 -101.7517202
## 404 136 Sep 2011 55-69,99 210.35284 8.347999 -74.3528438
## 405 158 Sep 2011 70-249,99 185.19554 8.347999 -27.1955404
## 406 78 Oct 2011 10-29,99 101.79329 8.347999 -23.7932932
## 407 131 Oct 2011 30-40,99 167.11914 8.347999 -36.1191359
## 408 180 Oct 2011 41-54,99 258.55172 8.347999 -78.5517202
## 409 124 Oct 2011 55-69,99 214.15284 8.347999 -90.1528438
## 410 129 Oct 2011 70-249,99 188.99554 8.347999 -59.9955404
## 411 58 Nov 2011 10-29,99 102.05484 8.563781 -44.0548437
## 412 114 Nov 2011 30-40,99 167.38069 8.563781 -53.3806864
## 413 178 Nov 2011 41-54,99 258.81327 8.563781 -80.8132706
## 414 174 Nov 2011 55-69,99 214.41439 8.563781 -40.4143942
## 415 130 Nov 2011 70-249,99 189.25709 8.563781 -59.2570909
## 416 82 Dec 2011 10-29,99 98.72627 8.563781 -16.7262722
## 417 138 Dec 2011 30-40,99 164.05211 8.563781 -26.0521149
## 418 204 Dec 2011 41-54,99 255.48470 8.563781 -51.4846992
## 419 153 Dec 2011 55-69,99 211.08582 8.563781 -58.0858228
## 420 135 Dec 2011 70-249,99 185.92852 8.563781 -50.9285194
## 421 72 Jan 2012 10-29,99 57.94983 8.349309 14.0501735
## 422 119 Jan 2012 30-40,99 123.27567 8.349309 -4.2756692
## 423 156 Jan 2012 41-54,99 214.70825 8.349309 -58.7082535
## 424 122 Jan 2012 55-69,99 170.30938 8.349309 -48.3093771
## 425 95 Jan 2012 70-249,99 145.15207 8.349309 -50.1520737
## 426 66 Feb 2012 10-29,99 68.86983 8.349309 -2.8698265
## 427 98 Feb 2012 30-40,99 134.19567 8.349309 -36.1956692
## 428 184 Feb 2012 41-54,99 225.62825 8.349309 -41.6282535
## 429 133 Feb 2012 55-69,99 181.22938 8.349309 -48.2293771
## 430 128 Feb 2012 70-249,99 156.07207 8.349309 -28.0720737
## 431 66 Mar 2012 10-29,99 94.38983 8.349309 -28.3898265
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## 481 86 Jan 2013 10-29,99 53.57303 8.389838 32.4269735
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## 522 160 Sep 2013 30-40,99 154.56554 8.389838 5.4344642
## 523 206 Sep 2013 41-54,99 245.99812 8.389838 -39.9981201
## 524 192 Sep 2013 55-69,99 201.59924 8.389838 -9.5992437
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## 527 162 Oct 2013 30-40,99 158.36554 8.389838 3.6344642
## 528 278 Oct 2013 41-54,99 249.79812 8.389838 28.2018799
## 529 228 Oct 2013 55-69,99 205.39924 8.389838 22.6007563
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## 533 256 Nov 2013 41-54,99 250.05967 8.634675 5.9403294
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## 536 94 Dec 2013 10-29,99 89.97267 8.634675 4.0273278
## 537 141 Dec 2013 30-40,99 155.29851 8.634675 -14.2985149
## 538 196 Dec 2013 41-54,99 246.73110 8.634675 -50.7310991
## 539 164 Dec 2013 55-69,99 202.33222 8.634675 -38.3322227
## 540 165 Dec 2013 70-249,99 177.17492 8.634675 -12.1749194
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## 542 133 Jan 2014 30-40,99 114.52207 8.469022 18.4779309
## 543 235 Jan 2014 41-54,99 205.95465 8.469022 29.0453466
## 544 157 Jan 2014 55-69,99 161.55578 8.469022 -4.5557770
## 545 135 Jan 2014 70-249,99 136.39847 8.469022 -1.3984736
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## 549 169 Feb 2014 55-69,99 172.47578 8.469022 -3.4757770
## 550 162 Feb 2014 70-249,99 147.31847 8.469022 14.6815264
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## 554 176 Mar 2014 55-69,99 197.99578 8.469022 -21.9957770
## 555 177 Mar 2014 70-249,99 172.83847 8.469022 4.1615264
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## 583 268 Sep 2014 41-54,99 241.62132 8.469022 26.3786799
## 584 196 Sep 2014 55-69,99 197.22244 8.469022 -1.2224437
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## 599 202 Dec 2014 55-69,99 197.95542 8.726513 4.0445773
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## 629 140 Jun 2014 55-69,99 179.95578 8.469022 -39.9557770
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## 643 268 Sep 2014 41-54,99 241.62132 8.469022 26.3786799
## 644 196 Sep 2014 55-69,99 197.22244 8.469022 -1.2224437
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## 658 257 Dec 2014 41-54,99 242.35430 8.726513 14.6457009
## 659 202 Dec 2014 55-69,99 197.95542 8.726513 4.0445773
## 660 176 Dec 2014 70-249,99 172.79812 8.726513 3.2018807
## 661 80 Jan 2015 10-29,99 44.81943 8.585790 35.1805736
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## 669 181 Feb 2015 55-69,99 168.09898 8.585790 12.9010230
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## 680 213 Apr 2015 70-249,99 164.35501 8.585790 48.6449931
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## 689 172 Jun 2015 55-69,99 175.57898 8.585790 -3.5789770
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## 695 179 Jul 2015 70-249,99 155.18167 8.585790 23.8183264
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## 699 189 Aug 2015 55-69,99 188.04564 8.585790 0.9543564
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## 709 222 Oct 2015 55-69,99 196.64564 8.585790 25.3543564
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## 714 209 Nov 2015 55-69,99 196.90719 8.854546 12.0928059
## 715 228 Nov 2015 70-249,99 171.74989 8.854546 56.2501093
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## 717 145 Dec 2015 30-40,99 146.54491 8.854546 -1.5449148
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## 721 80 Jan 2015 10-29,99 44.81943 8.585790 35.1805736
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## 723 186 Jan 2015 41-54,99 201.57785 8.585790 -15.5778534
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## 727 137 Feb 2015 30-40,99 121.06527 8.585790 15.9347309
## 728 261 Feb 2015 41-54,99 212.49785 8.585790 48.5021466
## 729 181 Feb 2015 55-69,99 168.09898 8.585790 12.9010230
## 730 155 Feb 2015 70-249,99 142.94167 8.585790 12.0583264
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## 736 127 Apr 2015 10-29,99 77.15276 8.585790 49.8472403
## 737 175 Apr 2015 30-40,99 142.47860 8.585790 32.5213976
## 738 268 Apr 2015 41-54,99 233.91119 8.585790 34.0888133
## 739 211 Apr 2015 55-69,99 189.51231 8.585790 21.4876897
## 740 213 Apr 2015 70-249,99 164.35501 8.585790 48.6449931
## 741 87 May 2015 10-29,99 80.17943 8.585790 6.8205736
## 742 167 May 2015 30-40,99 145.50527 8.585790 21.4947309
## 743 265 May 2015 41-54,99 236.93785 8.585790 28.0621466
## 744 234 May 2015 55-69,99 192.53898 8.585790 41.4610230
## 745 227 May 2015 70-249,99 167.38167 8.585790 59.6183264
## 746 100 Jun 2015 10-29,99 63.21943 8.585790 36.7805736
## 747 139 Jun 2015 30-40,99 128.54527 8.585790 10.4547309
## 748 254 Jun 2015 41-54,99 219.97785 8.585790 34.0221466
## 749 172 Jun 2015 55-69,99 175.57898 8.585790 -3.5789770
## 750 196 Jun 2015 70-249,99 150.42167 8.585790 45.5783264
## 751 110 Jul 2015 10-29,99 67.97943 8.585790 42.0205736
## 752 192 Jul 2015 30-40,99 133.30527 8.585790 58.6947309
## 753 253 Jul 2015 41-54,99 224.73785 8.585790 28.2621466
## 754 195 Jul 2015 55-69,99 180.33898 8.585790 14.6610230
## 755 179 Jul 2015 70-249,99 155.18167 8.585790 23.8183264
## 756 111 Aug 2015 10-29,99 75.68609 8.585790 35.3139069
## 757 148 Aug 2015 30-40,99 141.01194 8.585790 6.9880642
## 758 277 Aug 2015 41-54,99 232.44452 8.585790 44.5554800
## 759 189 Aug 2015 55-69,99 188.04564 8.585790 0.9543564
## 760 172 Aug 2015 70-249,99 162.88834 8.585790 9.1116597
## 761 113 Sep 2015 10-29,99 80.48609 8.585790 32.5139069
## 762 141 Sep 2015 30-40,99 145.81194 8.585790 -4.8119358
## 763 249 Sep 2015 41-54,99 237.24452 8.585790 11.7554800
## 764 177 Sep 2015 55-69,99 192.84564 8.585790 -15.8456436
## 765 170 Sep 2015 70-249,99 167.68834 8.585790 2.3116597
## 766 79 Oct 2015 10-29,99 84.28609 8.585790 -5.2860931
## 767 208 Oct 2015 30-40,99 149.61194 8.585790 58.3880642
## 768 260 Oct 2015 41-54,99 241.04452 8.585790 18.9554800
## 769 222 Oct 2015 55-69,99 196.64564 8.585790 25.3543564
## 770 189 Oct 2015 70-249,99 171.48834 8.585790 17.5116597
## 771 79 Nov 2015 10-29,99 84.54764 8.854546 -5.5476435
## 772 184 Nov 2015 30-40,99 149.87349 8.854546 34.1265138
## 773 278 Nov 2015 41-54,99 241.30607 8.854546 36.6939295
## 774 209 Nov 2015 55-69,99 196.90719 8.854546 12.0928059
## 775 228 Nov 2015 70-249,99 171.74989 8.854546 56.2501093
## 776 107 Dec 2015 10-29,99 81.21907 8.854546 25.7809279
## 777 145 Dec 2015 30-40,99 146.54491 8.854546 -1.5449148
## 778 291 Dec 2015 41-54,99 237.97750 8.854546 53.0225009
## 779 238 Dec 2015 55-69,99 193.57862 8.854546 44.4213773
## 780 295 Dec 2015 70-249,99 168.42132 8.854546 126.5786807
## 781 73 Jan 2016 10-29,99 40.44263 8.738638 32.5573736
## 782 118 Jan 2016 30-40,99 105.76847 8.738638 12.2315309
## 783 214 Jan 2016 41-54,99 197.20105 8.738638 16.7989467
## 784 146 Jan 2016 55-69,99 152.80218 8.738638 -6.8021769
## 785 133 Jan 2016 70-249,99 127.64487 8.738638 5.3551264
## 786 89 Feb 2016 10-29,99 51.36263 8.738638 37.6373736
## 787 128 Feb 2016 30-40,99 116.68847 8.738638 11.3115309
## 788 269 Feb 2016 41-54,99 208.12105 8.738638 60.8789467
## 789 210 Feb 2016 55-69,99 163.72218 8.738638 46.2778231
## 790 148 Feb 2016 70-249,99 138.56487 8.738638 9.4351264
## 791 102 Mar 2016 10-29,99 76.88263 8.738638 25.1173736
## 792 183 Mar 2016 30-40,99 142.20847 8.738638 40.7915309
## 793 276 Mar 2016 41-54,99 233.64105 8.738638 42.3589467
## 794 220 Mar 2016 55-69,99 189.24218 8.738638 30.7578231
## 795 205 Mar 2016 70-249,99 164.08487 8.738638 40.9151264
## 796 84 Apr 2016 10-29,99 72.77596 8.738638 11.2240403
## 797 190 Apr 2016 30-40,99 138.10180 8.738638 51.8981976
## 798 276 Apr 2016 41-54,99 229.53439 8.738638 46.4656133
## 799 171 Apr 2016 55-69,99 185.13551 8.738638 -14.1355103
## 800 209 Apr 2016 70-249,99 159.97821 8.738638 49.0217931
## 801 90 May 2016 10-29,99 75.80263 8.738638 14.1973736
## 802 172 May 2016 30-40,99 141.12847 8.738638 30.8715309
## 803 275 May 2016 41-54,99 232.56105 8.738638 42.4389467
## 804 209 May 2016 55-69,99 188.16218 8.738638 20.8378231
## 805 244 May 2016 70-249,99 163.00487 8.738638 80.9951264
## 806 79 Jun 2016 10-29,99 58.84263 8.738638 20.1573736
## 807 134 Jun 2016 30-40,99 124.16847 8.738638 9.8315309
## 808 231 Jun 2016 41-54,99 215.60105 8.738638 15.3989467
## 809 223 Jun 2016 55-69,99 171.20218 8.738638 51.7978231
## 810 229 Jun 2016 70-249,99 146.04487 8.738638 82.9551264
## 811 77 Jul 2016 10-29,99 63.60263 8.738638 13.3973736
## 812 166 Jul 2016 30-40,99 128.92847 8.738638 37.0715309
## 813 278 Jul 2016 41-54,99 220.36105 8.738638 57.6389467
## 814 174 Jul 2016 55-69,99 175.96218 8.738638 -1.9621769
## 815 198 Jul 2016 70-249,99 150.80487 8.738638 47.1951264
## 816 90 Aug 2016 10-29,99 71.30929 8.738638 18.6907070
## 817 177 Aug 2016 30-40,99 136.63514 8.738638 40.3648643
## 818 296 Aug 2016 41-54,99 228.06772 8.738638 67.9322800
## 819 240 Aug 2016 55-69,99 183.66884 8.738638 56.3311564
## 820 225 Aug 2016 70-249,99 158.51154 8.738638 66.4884598
## 821 104 Sep 2016 10-29,99 76.10929 8.738638 27.8907070
## 822 174 Sep 2016 30-40,99 141.43514 8.738638 32.5648643
## 823 288 Sep 2016 41-54,99 232.86772 8.738638 55.1322800
## 824 203 Sep 2016 55-69,99 188.46884 8.738638 14.5311564
## 825 189 Sep 2016 70-249,99 163.31154 8.738638 25.6884598
## 826 87 Oct 2016 10-29,99 79.90929 8.738638 7.0907070
## 827 154 Oct 2016 30-40,99 145.23514 8.738638 8.7648643
## 828 298 Oct 2016 41-54,99 236.66772 8.738638 61.3322800
## 829 222 Oct 2016 55-69,99 192.26884 8.738638 29.7311564
## 830 214 Oct 2016 70-249,99 167.11154 8.738638 46.8884598
## 831 70 Nov 2016 10-29,99 80.17084 9.017232 -10.1708435
## 832 164 Nov 2016 30-40,99 145.49669 9.017232 18.5033138
## 833 288 Nov 2016 41-54,99 236.92927 9.017232 51.0707295
## 834 252 Nov 2016 55-69,99 192.53039 9.017232 59.4696059
## 835 211 Nov 2016 70-249,99 167.37309 9.017232 43.6269093
## 836 87 Dec 2016 10-29,99 76.84227 9.017232 10.1577279
## 837 195 Dec 2016 30-40,99 142.16811 9.017232 52.8318852
## 838 296 Dec 2016 41-54,99 233.60070 9.017232 62.3993010
## 839 285 Dec 2016 55-69,99 189.20182 9.017232 95.7981774
## 840 272 Dec 2016 70-249,99 164.04452 9.017232 107.9554807
## 841 84 Jan 2017 10-29,99 36.06583 8.925712 47.9341737
## 842 152 Jan 2017 30-40,99 101.39167 8.925712 50.6083310
## 843 260 Jan 2017 41-54,99 192.82425 8.925712 67.1757467
## 844 211 Jan 2017 55-69,99 148.42538 8.925712 62.5746231
## 845 227 Jan 2017 70-249,99 123.26807 8.925712 103.7319265
## 846 70 Feb 2017 10-29,99 46.98583 8.925712 23.0141737
## 847 129 Feb 2017 30-40,99 112.31167 8.925712 16.6883310
## 848 221 Feb 2017 41-54,99 203.74425 8.925712 17.2557467
## 849 211 Feb 2017 55-69,99 159.34538 8.925712 51.6546231
## 850 232 Feb 2017 70-249,99 134.18807 8.925712 97.8119265
## 851 104 Mar 2017 10-29,99 72.50583 8.925712 31.4941737
## 852 201 Mar 2017 30-40,99 137.83167 8.925712 63.1683310
## 853 340 Mar 2017 41-54,99 229.26425 8.925712 110.7357467
## 854 312 Mar 2017 55-69,99 184.86538 8.925712 127.1346231
## 855 258 Mar 2017 70-249,99 159.70807 8.925712 98.2919265
## 856 103 Apr 2017 10-29,99 68.39916 8.925712 34.6008403
## 857 151 Apr 2017 30-40,99 133.72500 8.925712 17.2749976
## 858 267 Apr 2017 41-54,99 225.15759 8.925712 41.8424134
## 859 190 Apr 2017 55-69,99 180.75871 8.925712 9.2412898
## 860 187 Apr 2017 70-249,99 155.60141 8.925712 31.3985931
## 861 105 May 2017 10-29,99 71.42583 8.925712 33.5741737
## 862 174 May 2017 30-40,99 136.75167 8.925712 37.2483310
## 863 261 May 2017 41-54,99 228.18425 8.925712 32.8157467
## 864 242 May 2017 55-69,99 183.78538 8.925712 58.2146231
## 865 256 May 2017 70-249,99 158.62807 8.925712 97.3719265
## 866 97 Jun 2017 10-29,99 54.46583 8.925712 42.5341737
## 867 157 Jun 2017 30-40,99 119.79167 8.925712 37.2083310
## 868 259 Jun 2017 41-54,99 211.22425 8.925712 47.7757467
## 869 202 Jun 2017 55-69,99 166.82538 8.925712 35.1746231
## 870 199 Jun 2017 70-249,99 141.66807 8.925712 57.3319265
## 871 73 Jul 2017 10-29,99 59.22583 8.925712 13.7741737
## 872 155 Jul 2017 30-40,99 124.55167 8.925712 30.4483310
## 873 288 Jul 2017 41-54,99 215.98425 8.925712 72.0157467
## 874 203 Jul 2017 55-69,99 171.58538 8.925712 31.4146231
## 875 218 Jul 2017 70-249,99 146.42807 8.925712 71.5719265
## 876 91 Aug 2017 10-29,99 66.93249 8.925712 24.0675070
## 877 188 Aug 2017 30-40,99 132.25834 8.925712 55.7416643
## 878 354 Aug 2017 41-54,99 223.69092 8.925712 130.3090800
## 879 247 Aug 2017 55-69,99 179.29204 8.925712 67.7079564
## 880 253 Aug 2017 70-249,99 154.13474 8.925712 98.8652598
## 881 86 Sep 2017 10-29,99 71.73249 8.925712 14.2675070
## 882 155 Sep 2017 30-40,99 137.05834 8.925712 17.9416643
## 883 306 Sep 2017 41-54,99 228.49092 8.925712 77.5090800
## 884 230 Sep 2017 55-69,99 184.09204 8.925712 45.9079564
## 885 237 Sep 2017 70-249,99 158.93474 8.925712 78.0652598
## 886 48 Oct 2017 10-29,99 75.53249 8.925712 -27.5324930
## 887 63 Oct 2017 30-40,99 140.85834 8.925712 -77.8583357
## 888 108 Oct 2017 41-54,99 232.29092 8.925712 -124.2909200
## 889 98 Oct 2017 55-69,99 187.89204 8.925712 -89.8920436
## 890 138 Oct 2017 70-249,99 162.73474 8.925712 -24.7347402
## .hat .sigma .cooksd .std.resid
## 1 0.02134301 62.52077 1.867599e-04 -0.38155192
## 2 0.02134301 62.52597 3.964297e-07 0.01757903
## 3 0.02134301 62.52544 1.966600e-05 0.12381403
## 4 0.02134301 62.51808 2.833382e-04 0.46996380
## 5 0.02134301 62.49468 1.121045e-03 -0.93480995
## 6 0.02134301 62.51350 4.473885e-04 -0.59054678
## 7 0.02134301 62.52502 3.469645e-05 0.16445777
## 8 0.02134301 62.52598 1.809204e-07 0.01187560
## 9 0.02134301 62.51306 4.628529e-04 0.60066647
## 10 0.02134301 62.52447 5.422396e-05 -0.20559261
## 11 0.02134301 62.51314 4.602242e-04 -0.59895834
## 12 0.02134301 62.51775 2.950367e-04 0.47956766
## 13 0.02134301 62.48237 1.561965e-03 1.10343697
## 14 0.02134301 62.40704 4.256961e-03 1.82163641
## 15 0.02134301 62.52435 5.875173e-05 -0.21400416
## 16 0.02134301 62.52227 1.332092e-04 -0.32223966
## 17 0.02134301 62.52366 8.330496e-05 0.25482810
## 18 0.02134301 62.46245 2.274792e-03 1.33162744
## 19 0.02134301 62.44007 3.075565e-03 1.54836863
## 20 0.02134301 62.52537 2.214910e-05 -0.13139835
## 21 0.02134301 62.52329 9.641174e-05 -0.27414280
## 22 0.02134301 62.49475 1.118604e-03 0.93379178
## 23 0.02134301 62.38338 5.102786e-03 1.99441504
## 24 0.02134301 62.28052 8.776169e-03 2.61555805
## 25 0.02134301 62.52392 7.402772e-05 0.24021995
## 26 0.02134301 62.52584 5.337131e-06 -0.06450090
## 27 0.02134301 62.46794 2.078382e-03 1.27284225
## 28 0.02134301 62.33069 6.985203e-03 2.33346552
## 29 0.02134301 62.15883 1.311382e-02 3.19724962
## 30 0.02134301 62.51259 4.798917e-04 0.61162257
## 31 0.02134301 62.52591 2.533814e-06 -0.04444257
## 32 0.02134301 62.48647 1.415042e-03 1.05025950
## 33 0.02134301 62.30482 7.908717e-03 2.48293243
## 34 0.02134301 62.29784 8.157851e-03 2.52173683
## 35 0.02134301 62.50941 5.935552e-04 0.68020912
## 36 0.02134301 62.49275 1.190217e-03 0.96321890
## 37 0.02134301 62.40787 4.227304e-03 1.81527988
## 38 0.02134301 62.08812 1.563057e-02 3.49059391
## 39 0.02134301 62.18970 1.201440e-02 3.06029220
## 40 0.02134301 62.49408 1.142641e-03 0.94377126
## 41 0.02134301 62.49991 9.338991e-04 0.85322161
## 42 0.02134301 62.40745 4.242385e-03 1.81851510
## 43 0.02134301 62.18325 1.224425e-02 3.08942731
## 44 0.02134301 62.12556 1.429830e-02 3.33852065
## 45 0.02134301 62.48065 1.623445e-03 1.12494327
## 46 0.02134301 62.49665 1.050652e-03 0.90498504
## 47 0.02134301 62.34042 6.637690e-03 2.27468034
## 48 0.02134301 62.04045 1.732572e-02 3.67500113
## 49 0.02134301 62.25271 9.768120e-03 2.75941725
## 50 0.02134301 62.44182 3.013164e-03 1.53258030
## 51 0.02187882 62.51267 4.892023e-04 0.60975182
## 52 0.02187882 62.45923 2.451456e-03 1.36496313
## 53 0.02187882 61.96100 2.066502e-02 3.96302459
## 54 0.02187882 62.06920 1.672219e-02 3.56496605
## 55 0.02187882 62.38517 5.167870e-03 1.98182206
## 56 0.02187882 62.51914 2.513678e-04 0.43708274
## 57 0.02187882 62.36070 6.064899e-03 2.14694370
## 58 0.02187882 62.18927 1.233840e-02 3.06223290
## 59 0.02187882 62.07199 1.662042e-02 3.55410200
## 60 0.02187882 62.37503 5.539594e-03 2.05186052
## 61 0.02033987 62.50720 6.404349e-04 0.72414511
## 62 0.02033987 62.45917 2.277527e-03 1.36558849
## 63 0.02033987 62.12736 1.355158e-02 3.33106475
## 64 0.02033987 62.30523 7.515270e-03 2.48062091
## 65 0.02033987 62.49493 1.058707e-03 0.93105647
## 66 0.02033987 62.52554 1.506466e-05 0.11106257
## 67 0.02033987 62.51781 2.786441e-04 0.47765355
## 68 0.02033987 62.47315 1.801074e-03 1.21437789
## 69 0.02033987 62.40526 4.113314e-03 1.83520280
## 70 0.02033987 62.45563 2.397915e-03 1.40121576
## 71 0.02033987 62.49519 1.049983e-03 0.92721253
## 72 0.02033987 62.51173 4.861588e-04 0.63092419
## 73 0.02033987 62.35109 5.956194e-03 2.20837352
## 74 0.02033987 62.43604 3.065399e-03 1.58427872
## 75 0.02033987 62.48745 1.313649e-03 1.03711716
## 76 0.02033987 62.52080 1.769636e-04 -0.38065376
## 77 0.02033987 62.52521 2.661248e-05 0.14761510
## 78 0.02033987 62.52396 6.896339e-05 0.23762790
## 79 0.02033987 62.49438 1.077519e-03 0.93929175
## 80 0.02033987 62.51684 3.118390e-04 0.50530471
## 81 0.02033987 62.52202 1.350890e-04 -0.33258154
## 82 0.02033987 62.52257 1.165071e-04 0.30886184
## 83 0.02033987 62.45724 2.343107e-03 1.38510973
## 84 0.02033987 62.49962 8.991254e-04 0.85802167
## 85 0.02033987 62.52003 2.031705e-04 0.40786684
## 86 0.02033987 62.52308 9.900899e-05 -0.28472489
## 87 0.02033987 62.52590 2.752808e-06 -0.04747622
## 88 0.02033987 62.42145 3.562110e-03 1.70781879
## 89 0.02033987 62.48006 1.565637e-03 1.13222736
## 90 0.02033987 62.46425 2.104260e-03 1.31261628
## 91 0.02033987 62.52087 1.743676e-04 -0.37785135
## 92 0.02033987 62.52549 1.702906e-05 0.11808194
## 93 0.02033987 62.50629 6.717388e-04 0.74163176
## 94 0.02033987 62.49419 1.083958e-03 0.94209417
## 95 0.02033987 62.52085 1.752117e-04 0.37876482
## 96 0.02033987 62.52063 1.827030e-04 0.38677726
## 97 0.02033987 62.48320 1.458741e-03 1.09289179
## 98 0.02033987 62.30311 7.587392e-03 2.49249546
## 99 0.02033987 62.45252 2.503982e-03 1.43187037
## 100 0.02033987 62.51046 5.293590e-04 0.65835977
## 101 0.02033987 62.52576 7.594213e-06 -0.07885505
## 102 0.02033987 62.47771 1.645644e-03 1.16079651
## 103 0.02033987 62.39470 4.472664e-03 1.91368863
## 104 0.02033987 62.41104 3.916658e-03 1.79079527
## 105 0.02033987 62.48773 1.304382e-03 1.03345246
## 106 0.02033987 62.52592 2.288321e-06 -0.04328591
## 107 0.02033987 62.45832 2.306380e-03 1.37421131
## 108 0.02033987 62.16694 1.220967e-02 3.16184190
## 109 0.02033987 62.20491 1.092183e-02 2.99044517
## 110 0.02033987 62.43580 3.073577e-03 1.58639083
## 111 0.02094212 62.52413 6.506895e-05 0.22740771
## 112 0.02094212 62.39379 4.639718e-03 1.92027777
## 113 0.02094212 62.16029 1.281144e-02 3.19092976
## 114 0.02094212 62.36577 5.622036e-03 2.11380575
## 115 0.02094212 62.42487 3.549926e-03 1.67968525
## 116 0.02094212 62.52596 8.533564e-07 -0.02604255
## 117 0.02094212 62.49860 9.619362e-04 0.87436226
## 118 0.02094212 62.31025 7.566752e-03 2.45229669
## 119 0.02094212 62.36741 5.564422e-03 2.10294690
## 120 0.02094212 62.41828 3.781115e-03 1.73351744
## 121 0.01950485 62.52255 1.122665e-04 0.30974266
## 122 0.01950485 62.47903 1.533701e-03 1.14484368
## 123 0.01950485 62.42198 3.395662e-03 1.70348431
## 124 0.01950485 62.46934 1.850174e-03 1.25742524
## 125 0.01950485 62.50073 8.252459e-04 0.83978394
## 126 0.01950485 62.52352 8.066435e-05 0.26255282
## 127 0.01950485 62.46164 2.101365e-03 1.34006738
## 128 0.01950485 62.36897 5.124327e-03 2.09263884
## 129 0.01950485 62.44349 2.693934e-03 1.51729256
## 130 0.01950485 62.49226 1.101838e-03 0.97036404
## 131 0.01950485 62.52568 1.002094e-05 0.09254013
## 132 0.01950485 62.50127 8.074419e-04 0.83067573
## 133 0.01950485 62.20864 1.034339e-02 2.97308481
## 134 0.01950485 62.36190 5.354716e-03 2.13916408
## 135 0.01950485 62.49817 9.085602e-04 0.88115585
## 136 0.01950485 62.52526 2.384406e-05 0.14274667
## 137 0.01950485 62.46073 2.131205e-03 1.34954844
## 138 0.01950485 62.31215 6.975274e-03 2.44149886
## 139 0.01950485 62.43706 2.903693e-03 1.57525633
## 140 0.01950485 62.51054 5.045286e-04 0.65662705
## 141 0.01950485 62.52577 7.059571e-06 0.07767210
## 142 0.01950485 62.49614 9.749311e-04 0.91277312
## 143 0.01950485 62.33698 6.166634e-03 2.29561978
## 144 0.01950485 62.41385 3.660869e-03 1.76875620
## 145 0.01950485 62.42744 3.217417e-03 1.65817204
## 146 0.01950485 62.52535 2.071967e-05 -0.13306607
## 147 0.01950485 62.51993 1.977994e-04 0.41113870
## 148 0.01950485 62.49558 9.932240e-04 0.92129663
## 149 0.01950485 62.51616 3.209571e-04 0.52372027
## 150 0.01950485 62.52241 1.169746e-04 0.31617070
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## 744 0.01887719 62.50992 5.078065e-04 0.66983319
## 745 0.01887719 62.49275 1.049972e-03 0.96317772
## 746 0.01887719 62.51334 3.996274e-04 0.59421710
## 747 0.01887719 62.52496 3.228821e-05 0.16890383
## 748 0.01887719 62.51517 3.419335e-04 0.54965269
## 749 0.01887719 62.52587 3.783869e-06 -0.05782099
## 750 0.01887719 62.50657 6.136701e-04 0.73635124
## 751 0.01887719 62.50948 5.216055e-04 0.67887314
## 752 0.01887719 62.49378 1.017692e-03 0.94825636
## 753 0.01887719 62.51852 2.359546e-04 0.45659567
## 754 0.01887719 62.52398 6.349606e-05 0.23685956
## 755 0.01887719 62.52068 1.675872e-04 0.38480250
## 756 0.01887719 62.51433 3.683916e-04 0.57052203
## 757 0.01887719 62.52553 1.442554e-05 0.11289729
## 758 0.01887719 62.50743 5.864358e-04 0.71982641
## 759 0.01887719 62.52598 2.690540e-07 0.01541833
## 760 0.01887719 62.52521 2.452524e-05 0.14720554
## 761 0.01887719 62.51610 3.122889e-04 0.52528598
## 762 0.01887719 62.52577 6.840028e-06 -0.07774035
## 763 0.01887719 62.52469 4.082244e-05 0.18991839
## 764 0.01887719 62.52364 7.417166e-05 -0.25599798
## 765 0.01887719 62.52594 1.578578e-06 0.03734656
## 766 0.01887719 62.52572 8.254444e-06 -0.08540070
## 767 0.01887719 62.49411 1.007086e-03 0.94330193
## 768 0.01887719 62.52263 1.061421e-04 0.30623966
## 769 0.01887719 62.51998 1.898993e-04 0.40961819
## 770 0.01887719 62.52312 9.058846e-05 0.28291369
## 771 0.02007748 62.52570 9.693278e-06 -0.08968112
## 772 0.02007748 62.51509 3.668068e-04 0.55167638
## 773 0.02007748 62.51338 4.240744e-04 0.59318026
## 774 0.02007748 62.52462 4.605828e-05 0.19548775
## 775 0.02007748 62.49637 9.965528e-04 0.90931810
## 776 0.02007748 62.51976 2.093393e-04 0.41676478
## 777 0.02007748 62.52596 7.517313e-07 -0.02497451
## 778 0.02007748 62.49967 8.854703e-04 0.85714180
## 779 0.02007748 62.50752 6.214950e-04 0.71809927
## 780 0.02007748 62.37586 5.046319e-03 2.04622333
## 781 0.01955529 62.51607 3.248213e-04 0.52617007
## 782 0.01955529 62.52459 4.584662e-05 0.19767766
## 783 0.01955529 62.52335 8.647883e-05 0.27149312
## 784 0.01955529 62.52555 1.417887e-05 -0.10993215
## 785 0.01955529 62.52572 8.787902e-06 0.08654590
## 786 0.01955529 62.51273 4.340946e-04 0.60826957
## 787 0.01955529 62.52479 3.920925e-05 0.18280925
## 788 0.01955529 62.49131 1.135743e-03 0.98388403
## 789 0.01955529 62.50595 6.562836e-04 0.74791062
## 790 0.01955529 62.52515 2.727980e-05 0.15248408
## 791 0.01955529 62.52008 1.933277e-04 0.40592987
## 792 0.01955529 62.51042 5.099009e-04 0.65924491
## 793 0.01955529 62.50920 5.498396e-04 0.68457641
## 794 0.01955529 62.51714 2.899058e-04 0.49708696
## 795 0.01955529 62.51033 5.129955e-04 0.66124238
## 796 0.01955529 62.52481 3.860505e-05 0.18139529
## 797 0.01955529 62.50079 8.253730e-04 0.83874328
## 798 0.01955529 62.50579 6.616207e-04 0.75094556
## 799 0.01955529 62.52412 6.123063e-05 -0.22844848
## 800 0.01955529 62.50350 7.364175e-04 0.79225680
## 801 0.01955529 62.52410 6.176775e-05 0.22944827
## 802 0.01955529 62.51707 2.920533e-04 0.49892463
## 803 0.01955529 62.50914 5.519185e-04 0.68586932
## 804 0.01955529 62.52192 1.330609e-04 0.33676669
## 805 0.01955529 62.46459 2.010312e-03 1.30898801
## 806 0.01955529 62.52218 1.245127e-04 0.32576973
## 807 0.01955529 62.52508 2.962020e-05 0.15889050
## 808 0.01955529 62.52377 7.266541e-05 0.24886728
## 809 0.01955529 62.50089 8.221835e-04 0.83712110
## 810 0.01955529 62.46159 2.108784e-03 1.34066419
## 811 0.01955529 62.52431 5.500283e-05 0.21651922
## 812 0.01955529 62.51313 4.211403e-04 0.59912481
## 813 0.01955529 62.49490 1.018070e-03 0.93152136
## 814 0.01955529 62.52595 1.179837e-06 -0.03171137
## 815 0.01955529 62.50515 6.825587e-04 0.76273545
## 816 0.01955529 62.52272 1.070526e-04 0.30206646
## 817 0.01955529 62.51074 4.992898e-04 0.65234941
## 818 0.01955529 62.48281 1.414159e-03 1.09787519
## 819 0.01955529 62.49630 9.723958e-04 0.91038574
## 820 0.01955529 62.48462 1.354685e-03 1.07454115
## 821 0.01955529 62.51871 2.383772e-04 0.45075059
## 822 0.01955529 62.51607 3.249707e-04 0.52629113
## 823 0.01955529 62.49755 9.314459e-04 0.89101032
## 824 0.01955529 62.52401 6.470623e-05 0.23484264
## 825 0.01955529 62.51981 2.022190e-04 0.41515937
## 826 0.01955529 62.52552 1.540724e-05 0.11459517
## 827 0.01955529 62.52527 2.354161e-05 0.14165176
## 828 0.01955529 62.49079 1.152720e-03 0.99121049
## 829 0.01955529 62.51772 2.708753e-04 0.48049468
## 830 0.01955529 62.50542 6.737172e-04 0.75777932
## 831 0.02082204 62.52502 3.384088e-05 -0.16448053
## 832 0.02082204 62.52278 1.120022e-04 0.29923131
## 833 0.02082204 62.50155 8.532412e-04 0.82590402
## 834 0.02082204 62.49285 1.156959e-03 0.96172871
## 835 0.02082204 62.50816 6.226394e-04 0.70552428
## 836 0.02082204 62.52502 3.375366e-05 0.16426843
## 837 0.02082204 62.49984 9.131033e-04 0.85438502
## 838 0.02082204 62.48951 1.273759e-03 1.00910706
## 839 0.02082204 62.43998 3.002218e-03 1.54922596
## 840 0.02082204 62.41674 3.812563e-03 1.74583106
## 841 0.02040151 62.50447 7.358417e-04 0.77501396
## 842 0.02040151 62.50200 8.202343e-04 0.81825053
## 843 0.02040151 62.48373 1.445170e-03 1.08611743
## 844 0.02040151 62.48932 1.253979e-03 1.01172510
## 845 0.02040151 62.42517 3.446028e-03 1.67716861
## 846 0.02040151 62.52103 1.696230e-04 0.37210000
## 847 0.02040151 62.52338 8.919073e-05 0.26982189
## 848 0.02040151 62.52320 9.535894e-05 0.27899604
## 849 0.02040151 62.50100 8.545005e-04 0.83516729
## 850 0.02040151 62.43636 3.063921e-03 1.58145229
## 851 0.02040151 62.51670 3.176540e-04 0.50920716
## 852 0.02040151 62.48862 1.277888e-03 1.02132434
## 853 0.02040151 62.41109 3.927079e-03 1.79040846
## 854 0.02040151 62.37449 5.176326e-03 2.05555036
## 855 0.02040151 62.43548 3.094066e-03 1.58921307
## 856 0.02040151 62.51478 3.834133e-04 0.55943667
## 857 0.02040151 62.52319 9.557183e-05 0.27930729
## 858 0.02040151 62.50959 5.606959e-04 0.67652057
## 859 0.02040151 62.52519 2.735011e-05 0.14941592
## 860 0.02040151 62.51676 3.157289e-04 0.50766178
## 861 0.02040151 62.51543 3.609978e-04 0.54283722
## 862 0.02040151 62.51300 4.443320e-04 0.60224208
## 863 0.02040151 62.51590 3.448724e-04 0.53057474
## 864 0.02040151 62.49425 1.085321e-03 0.94123132
## 865 0.02040151 62.43716 3.036417e-03 1.57433824
## 866 0.02040151 62.50905 5.793886e-04 0.68770516
## 867 0.02040151 62.51302 4.433782e-04 0.60159535
## 868 0.02040151 62.50461 7.309857e-04 0.77245247
## 869 0.02040151 62.51440 3.962350e-04 0.56871376
## 870 0.02040151 62.49521 1.052657e-03 0.92695962
## 871 0.02040151 62.52421 6.076102e-05 0.22270493
## 872 0.02040151 62.51731 2.969073e-04 0.49229766
## 873 0.02040151 62.47742 1.660921e-03 1.16437199
## 874 0.02040151 62.51675 3.160513e-04 0.50792096
## 875 0.02040151 62.47801 1.640512e-03 1.15719617
## 876 0.02040151 62.52056 1.855052e-04 0.38913060
## 877 0.02040151 62.49689 9.950703e-04 0.90124779
## 878 0.02040151 62.36682 5.438051e-03 2.10687593
## 879 0.02040151 62.48305 1.468160e-03 1.09472236
## 880 0.02040151 62.43442 3.130267e-03 1.59848290
## 881 0.02040151 62.52408 6.519137e-05 0.23068129
## 882 0.02040151 62.52297 1.030907e-04 0.29008616
## 883 0.02040151 62.46972 1.923973e-03 1.25318984
## 884 0.02040151 62.50625 6.749473e-04 0.74225348
## 885 0.02040151 62.46891 1.951684e-03 1.26218232
## 886 0.02040151 62.51889 2.427644e-04 -0.44515353
## 887 0.02040151 62.46921 1.941351e-03 -1.25883671
## 888 0.02040151 62.38120 4.947351e-03 -2.00957253
## 889 0.02040151 62.45029 2.587834e-03 -1.45340127
## 890 0.02040151 62.52026 1.959335e-04 -0.39991863predicted_trans2 %>%
ggplot(aes(factor(month, levels = month.abb), .resid, group = year)) +
geom_hline(yintercept = 0, colour = "white", size = 3) +
geom_line() +
facet_wrap(~ area)
For some apartement size classes, few years may have large influence on average number of transactions. We can look at the large cook’s distance.
predicted_trans2 %>%
arrange(desc(.cooksd)) %>%
dplyr::select(.cooksd, everything()) %>%
head()## .cooksd transactions month year area .fitted .se.fit .resid
## 1 0.02066502 530 Nov 2005 41-54,99 285.0741 9.243226 244.9259
## 2 0.01732572 512 Oct 2005 41-54,99 284.8125 9.129342 227.1875
## 3 0.01672219 461 Nov 2005 55-69,99 240.6752 9.243226 220.3248
## 4 0.01662042 457 Dec 2005 55-69,99 237.3466 9.243226 219.6534
## 5 0.01563057 492 Aug 2005 41-54,99 276.2125 9.129342 215.7875
## 6 0.01429830 443 Sep 2005 55-69,99 236.6136 9.129342 206.3864
## .hat .sigma .std.resid
## 1 0.02187882 61.96100 3.963025
## 2 0.02134301 62.04045 3.675001
## 3 0.02187882 62.06920 3.564966
## 4 0.02187882 62.07199 3.554102
## 5 0.02134301 62.08812 3.490594
## 6 0.02134301 62.12556 3.338521Same for mean price per m^2:
predicted_pua2 <- harju %>%
lm(price_unit_area_mean ~ month + year + area, data = .) %>%
augment
predicted_pua2 %>%
ggplot(aes(factor(month, levels = month.abb), .resid, group = year, color = factor(year))) +
geom_hline(yintercept = 0, colour = "white", size = 3) +
geom_line() +
facet_wrap(~ area) +
scale_color_viridis(discrete = TRUE) +
theme(axis.text.x = element_text(angle = 90, vjust = 0.5))
Seems ok!
predicted_pua2 %>%
arrange(desc(.cooksd)) %>%
dplyr::select(.cooksd, everything(.)) %>%
head()## .cooksd price_unit_area_mean month year area .fitted .se.fit
## 1 0.009230944 1725.98 Apr 2007 10-29,99 1043.973 34.24826
## 2 0.008394703 421.50 Jul 2009 10-29,99 1093.030 33.20911
## 3 0.007883079 1650.16 Jun 2007 30-40,99 1019.909 34.24826
## 4 0.006989624 1665.78 Aug 2007 10-29,99 1072.318 34.24826
## 5 0.006803107 1604.90 Apr 2007 30-40,99 1019.410 34.24826
## 6 0.006686472 1615.97 Apr 2007 41-54,99 1035.521 34.24826
## .resid .hat .sigma .std.resid
## 1 682.0070 0.01950485 244.2558 2.808659
## 2 -671.5304 0.01833919 244.2911 -2.763871
## 3 630.2512 0.01950485 244.4184 2.595517
## 4 593.4616 0.01950485 244.5261 2.444009
## 5 585.4899 0.01950485 244.5485 2.411179
## 6 580.4493 0.01950485 244.5626 2.390421Robust lm fit to number of transactions. Play with weights: price_min, price_unit_area_mean etc..
# install.packages("MASS")
library(MASS)##
## Attaching package: 'MASS'## The following object is masked from 'package:dplyr':
##
## selectpredicted_transa_robust <- harju %>%
rlm(transactions ~ month + area, data = ., weights = price_min) %>%
augmentAdd robust fit to plot:
p + geom_line(data = predicted_transa, aes(month, .fitted, group = 1),
color = "red",
size = 1) +
geom_line(data = predicted_transa_robust, aes(month, .fitted, group = 1),
color = "blue",
size = 1) +
labs(caption = "Red line: model fit of seasonal effect to number of transactions.\nBlue line: robust model fit of seasonal effect to number of transactions, weighted for minimal price. \nSource: Estonian Land Board, transactions database.")
## Whole dataset: all counties
Plot whole dataset:
apartments %>%
ggplot(aes(date, transactions, group = area, color = area)) +
geom_line() +
facet_wrap(~ county, scales = "free_y")
apartments %>%
mutate(price_unit_area_mean = price_unit_area_mean / consumerindex) %>%
ggplot(aes(date, price_unit_area_mean, group = area, color = area)) +
geom_line() +
facet_wrap(~ county, scales = "free_y")## Warning: Removed 8 rows containing missing values (geom_path).
Fit multiple models
Fit model for each county. Goodness of model fit is evaluated by its ability to predict response values. Response values can be predicted using the same data that was used to train model. In this case we are dealing with in-sample analysis, which is ok when all we want to know is model coeficients (eg. intercept and slope) to describe present data. In cases when we want to predict using some unseen future data, such models are usually overfitted, overly optimistic and don’t perform very well. To manage overfitting, we split dataset into training set for model fitting and test set for model performance assessment.
Resampling can be performed very well using base R function sample(). Let’s say we want to use approx. 70% of rows from “mtcars” table to be used in model training and leave remaining 30% for model testing. Basically, all we need to do is to generate to non-overlapping row indexes.
set.seed(123)
index <- sample(1:nrow(mtcars), floor(0.7 * nrow(mtcars)), replace = FALSE)
index## [1] 10 25 13 26 27 2 14 23 29 11 22 32 24 31 28 16 4 1 5 30 19 8## ~70% data goes to training set
train <- mtcars[index, ]
## remaining ~30% will be used for testing model performance
test <- mtcars[-index, ]Index based resampling is also implemented in tidyverse. We can use resample_partition() function from “modelr” library to perform. Here we generate data splits and move them to separate columns.
library(modelr)##
## Attaching package: 'modelr'## The following object is masked from 'package:broom':
##
## bootstrap## Generate data splits and move into separate columns
trans <- apartments %>%
group_by(county) %>%
nest %>%
mutate(parts = map(data, ~resample_partition(.x, c(test = 0.3, train = 0.7))),
test = map(parts, "test"),
train = map(parts, "train")) %>%
dplyr::select(-parts)Fit model to each data split. Let’s start with number of transactions.
## Fit model
trans <- trans %>%
mutate(mod_train = map(train, ~lm(transactions ~ month + area, data = .x)))
## Print data with new model column
trans %>%
dplyr::select(mod_train, everything())## # A tibble: 15 x 5
## mod_train county data test
## <list> <chr> <list> <list>
## 1 <S3: lm> Harju maakond <tibble [890 x 18]> <S3: resample>
## 2 <S3: lm> Hiiu maakond <tibble [400 x 18]> <S3: resample>
## 3 <S3: lm> Ida-Viru maakond <tibble [890 x 18]> <S3: resample>
## 4 <S3: lm> Jõgeva maakond <tibble [798 x 18]> <S3: resample>
## 5 <S3: lm> Järva maakond <tibble [824 x 18]> <S3: resample>
## 6 <S3: lm> Lääne maakond <tibble [832 x 18]> <S3: resample>
## 7 <S3: lm> Lääne-Viru maakond <tibble [884 x 18]> <S3: resample>
## 8 <S3: lm> Põlva maakond <tibble [738 x 18]> <S3: resample>
## 9 <S3: lm> Pärnu maakond <tibble [889 x 18]> <S3: resample>
## 10 <S3: lm> Rapla maakond <tibble [797 x 18]> <S3: resample>
## 11 <S3: lm> Saare maakond <tibble [786 x 18]> <S3: resample>
## 12 <S3: lm> Tartu maakond <tibble [890 x 18]> <S3: resample>
## 13 <S3: lm> Valga maakond <tibble [847 x 18]> <S3: resample>
## 14 <S3: lm> Viljandi maakond <tibble [875 x 18]> <S3: resample>
## 15 <S3: lm> Võru maakond <tibble [832 x 18]> <S3: resample>
## # ... with 1 more variables: train <list>coef() and summary() return vector and S3 object respectively. Model coeficients and summary statistics can be returned as a data frame using tidy() function from “broom” library:
## model coeficients
trans %>%
mutate(mod_tidy = map(mod_train, tidy)) %>%
dplyr::select(county, mod_tidy) %>%
unnest %>%
head()## # A tibble: 6 x 6
## county term estimate std.error statistic p.value
## <chr> <chr> <dbl> <dbl> <dbl> <dbl>
## 1 Harju maakond (Intercept) 90.720597 10.95902 8.2781703 7.956235e-16
## 2 Harju maakond monthAug 8.425303 12.99468 0.6483655 5.169934e-01
## 3 Harju maakond monthDec 7.407290 12.87110 0.5754980 5.651675e-01
## 4 Harju maakond monthFeb -19.712457 13.36976 -1.4744058 1.408899e-01
## 5 Harju maakond monthJan -34.256393 12.75323 -2.6860961 7.426733e-03
## 6 Harju maakond monthJul -11.766739 13.05168 -0.9015499 3.676530e-01Pseudo out-of-sample model performance, augment() adds predictions to original data frame (.fitted). We subtract fitted values from the original values and calculate root-mean-squared deviation (rmsd). Smaller rmsd indicates better fit.
trans <- trans %>%
mutate(mod_pred = map2(mod_train, test, ~augment(.x, newdata = .y)),
mod_pred = map(mod_pred, ~mutate(.x, .resid = transactions - .fitted)),
mod_rmsd = map_dbl(mod_pred, ~sqrt(mean(.x$`.resid`^2))))
trans %>%
dplyr::select(county, mod_rmsd) %>%
arrange(desc(mod_rmsd))## # A tibble: 15 x 2
## county mod_rmsd
## <chr> <dbl>
## 1 Harju maakond 66.4419493
## 2 Tartu maakond 16.5692863
## 3 Ida-Viru maakond 9.7488850
## 4 Pärnu maakond 9.2678223
## 5 Lääne-Viru maakond 4.8961802
## 6 Viljandi maakond 3.5521556
## 7 Järva maakond 3.1063724
## 8 Rapla maakond 2.9415115
## 9 Valga maakond 2.9113005
## 10 Lääne maakond 2.7434744
## 11 Saare maakond 2.5359518
## 12 Jõgeva maakond 2.4825984
## 13 Võru maakond 2.3033747
## 14 Põlva maakond 1.9872345
## 15 Hiiu maakond 0.7937306We can see that Harju county displays worst fit and Tartu is next. These two counties show also majority of transactions.
trans_pred <- trans %>%
dplyr::select(county, mod_pred) %>%
unnest
trans_pred %>%
dplyr::select(.fitted, transactions, everything()) %>%
head()## # A tibble: 6 x 22
## .fitted transactions county date year month area
## <dbl> <int> <chr> <date> <int> <chr> <chr>
## 1 136.5889 175 Harju maakond 2005-02-01 2005 Feb 30-40,99
## 2 221.3443 257 Harju maakond 2005-02-01 2005 Feb 41-54,99
## 3 244.3975 350 Harju maakond 2005-03-01 2005 Mar 41-54,99
## 4 90.7206 101 Harju maakond 2005-04-01 2005 Apr 10-29,99
## 5 241.0568 360 Harju maakond 2005-04-01 2005 Apr 41-54,99
## 6 199.9944 329 Harju maakond 2005-04-01 2005 Apr 55-69,99
## # ... with 15 more variables: area_total <dbl>, area_mean <dbl>,
## # price_total <int>, price_min <dbl>, price_max <dbl>,
## # price_unit_area_min <dbl>, price_unit_area_max <dbl>,
## # price_unit_area_median <dbl>, price_unit_area_mean <dbl>,
## # price_unit_area_sd <dbl>, title <chr>, subtitle <chr>,
## # consumerindex <dbl>, .se.fit <dbl>, .resid <dbl>